Cheometría

• Circumferencia d'o cerclo de radio r: ${\displaystyle C=2\pi r}$
• Aria d'o cerclo de radio r: ${\displaystyle A=\pi r^{2}}$
• Aria d'a elipse con semieixes a y b: ${\displaystyle A=\pi ab}$
• Volumen d'a esfera de radio r: ${\displaystyle A=frac{4}{3}\pi r^{3}}$
• Aria d'a superficie d'una esfera de radio r: ${\displaystyle A=4\pi r^{2}}$
• Anglos: 180 graus son equivalents a ${\displaystyle \pi }$ radians

Analís

${\displaystyle {\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots ={\frac {\pi }{4}}}$ (Formula de Leibniz)

${\displaystyle {\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots ={\frac {\pi }{2}}}$ (producto de Wallis)

${\displaystyle \zeta (2)={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots ={\frac {\pi ^{2}}{6}}}$ (Euler)

${\displaystyle \zeta (4)={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+\cdots ={\frac {\pi ^{4}}{90}}}$

${\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}dx={\sqrt {\pi }}}$ (integral de Gauss)

${\displaystyle \Gamma \left({1 \over 2}\right)={\sqrt {\pi }}}$

${\displaystyle n!\approx {\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}}$ (Formula de Stirling)

${\displaystyle e^{\pi i}+1=0\;}$ (Identitat d'Euler)

π tiene una representación en fraccions continas con propiedaz bien bonicas:

${\displaystyle {\frac {4}{\pi }}=1+{\frac {1}{3+{\frac {4}{5+{\frac {9}{7+{\frac {16}{9+{\frac {25}{11+{\frac {36}{13+...}}}}}}}}}}}}}$

(Se'n puede veyer atras 12 representacions en )

Teoría de numeros

A probalidat de que dos numeros trigaus aliatoriament sigan primos entre éls ye de 6/π².

A probalidat de que un entero trigau aliatoriament no tienga garra factor primo elevau a una potencia superior a 1 ye de 6/π².